Answer: D
Step-by-step explanation:
S is between B and C. True or false
I would say false.
B is on top of S.
I'm using common sense here but If you were to draw a line from B and C.
S would not be marked in between that line.
The claim "S is between B and C" is false.
Is the statement true or false?S is between B and C only if the 3 points are collinear, and S is between the other poitns in that line.
In the triangle we can see that CS and SB are perependicular lines, so the 3 points are not collinear, and thus, the statement "S is between B and C" is false.
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Barry runs at an average rate of 8 mi/hr. He walks at an average rate of 3 mi/hr. If x represents the time spent running and y represents the time spent walking, write a linear equation that relates the time he could spend running and walking if he travels a total distance of 16 miles
============================
Work Shown:
x = number of hours spent running
8x = distance he runs (since he runs at 8 mph)
y = number of hours spent walking
3y = distance he walks (he walks at a speed of 3 mph)
8x+3y = total distance = 16 miles
8x+3y = 16
This equation is in standard form Ax+By = C
--------
Extra Info
Solving for y will get
8x+3y = 16
3y = -8x+16
y = (-8x+16)/3
y = (-8x)/3+16/3
y = (-8/3)x+16/3
This is in slope intercept form y = mx+b
m = -8/3 is the slope
b = 16/3 is the y intercept
Tony sells 50.5 ounces of lemonade for a total of $20.20. Find the unit price in dollars per ounce. If necessary, round your answer to the nearest cent.
The unit price in dollars per ounce will be $0.4 per ounce.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Division means the separation of something into different parts, sharing of something among different people, places, etc.
Tony sells 50.5 ounces of lemonade for a total of $20.20.
The unit price in dollars per ounce will be calculated as,
Rate = $20.20 / 50.5
Rate = $0.4 per ounce
The unit price in dollars per ounce will be $0.4 per ounce.
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Tony's lemonade has a unit price of $0.40 per ounce.
Tony sells 50.5 ounces of lemonade for a total of $20.20.
To find the unit price in dollars per ounce, we divide the total cost by the total number of ounces.
The calculation looks like this: $20.20 ÷ 50.5 ounces = $0.40 per ounce.
Therefore, the unit price of Tony’s lemonade is $0.40 per ounce. If rounding is necessary, this answer is already precise to the nearest cent.
Maria ordered a pizza. She ate 2/9 of it and gave the remaining pizza to her 3 brothers. What fraction of the whole pizza will each of Maria's brothers receive if they share the remaining pizza equally?
A. 7/9
B. 3/7
C. 1/3
D. 7/27
E. 2/27
Answer:
D 7/27
Step-by-step explanation:
If Maria ate 2/9 of the pizza, that means she DIDN'T eat 7/9 of the pizza. So far so good? Ok, then you just need to find out what is 1/3 of 7/9, because the three brothers are dividing the leftover pizza equally, right? Hint - "of" usually means multiply. And remember multiplying fractions is lovely - you simply multiply the numerators together, then multiply the denominators together (no common denominator mumbo jumbo). So...
1/3 * 7/9 = 7/27.
Maria's brothers will each receive option D. 7/27 of the pizza.
To determine the fraction of the whole pizza each of Maria's brothers will receive, if they share the remaining pizza equally, follow these steps:
Maria ate 2/9 of the pizza, so the remaining fraction of the pizza is 1 - 2/9 = 7/9.The remaining pizza (7/9) is shared equally among her 3 brothers.To find the fraction each brother gets, divide 7/9 by 3. This can be done by multiplying 7/9 by the reciprocal of 3 (which is 1/3): (7/9) * (1/3) = 7/27Therefore, each of Maria's brothers will receive option D. 7/27 of the whole pizza.
Ena's income is $1900 a month, and she plans to budget 29 of her income for entertainment and 15 of her income for groceries. Step 1 of 2 : What fraction of her income does she plan to spend each month on these two items together? Express your answer in lowest terms.
Answer:
2/10 of her income will go to these items
Step-by-step explanation:
29 +15 = 41
41/1900 equal 2/10
Final answer:
Ena plans to spend 29% of her income on entertainment and 15% on groceries, which is a total of [tex]\(\frac{44}{100}\)[/tex]of her income. Simplifying this to its lowest terms gives us [tex]\(\frac{11}{25}\)[/tex] of her income spent on these two items together.
Explanation:
To find the fraction of Ena's income that is spent on entertainment and groceries together, we need to sum the fractions of income allocated to each category. Ena plans to spend 29% of her income on entertainment and 15% on groceries. In fractional terms, 29% is the same as 29/100 and 15% is equivalent to 15/100. Adding these fractions together:
[tex]\(\frac{29}{100} + \frac{15}{100} = \frac{44}{100}\)[/tex]
Now, we simplify the fraction to its lowest terms:
[tex]\(\frac{44}{100} = \frac{44 \div 4}{100 \div 4} = \frac{11}{25}\)[/tex]
Thus, Ena plans to spend [tex]\(\frac{11}{25}\)[/tex]of her income on entertainment and groceries together.
Demont used 4 gallons of gasoline in three days driving to work .Each day he used the same amount of gasoline. How many gallons of gasoline did he use each day?
Answer:
1 1/3 gallons per day
Step-by-step explanation:
To find gallons per day, divide gallons by days. ("per" means "divided by")
(4 gal)/(3 day) = (4/3) gal/day
Demont used 4/3 = 1 1/3 gallon each day.
To find out how many gallons of gasoline Demonte used each day, divide the total amount used (4 gallons) by the number of days (3), yielding approximately 1.33 gallons per day.
Demonte used 4 gallons of gasoline in three days driving to work and used the same amount of gasoline each day. To calculate the amount of gasoline he used each day, you divide the total gallons of gasoline by the number of days. This can be represented by the following equation:
Gallons per day = Total gallons used ÷ Number of days
Gallons per day = 4 gallons ÷ 3 days
Gallons per day = 1.33 gallons per day (approximately)
Therefore, Demonte used approximately 1.33 gallons of gasoline each day.
The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
Answer:
Step-by-step explanation:
x+x+(x+12)=180
3x=180-12=168
x=56
third angle=56+12=68
so angles are 56°,56°,68°
The larger angle is x + 12 i.e. 56 + 12 = 68⁰.
What is Triangle?A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.
Let the first angle be x.
then second angle is equal to first i.e. x
and third angle = x + 12
we know that,
Sum of all angles of a triangle is 180⁰.
Now,
x + x + x + 12 = 180
3x = 180 -12
3x = 168
x = 168/3
x = 56
Thus, the larger angle is x + 12 i.e. 56 + 12 = 68⁰.
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-5=x-3y
11=-3x+7y
This will be elimination
Answer:
Step-by-step explanation:
The given system of simultaneous equations is expressed as
-5=x-3y
11=-3x+7y
Rearranging both equations, it becomes
x - 3y = - 5- - - - - - - - - - 1
- 3x + 7y = 11 - - - - - - - - - -2
Multiplying equation 1 by 3 and equation 2 by1, it becomes
3x - 9y = - 15 - - - - - - - - - - -3
- 3x + 7y = 11 - - - - - - - - - - - 4
Adding equation 3 to equation 4, it becomes
- 2y = - 4
Dividing the left hand side and the right hand side of the equation by
- 2, it becomes
- 2y/ - 2 = - 4y/- 2
y = 2
Substituting y = 2 into equation 1, it becomes
x - 3 × 2= - 5
x - 6 = - 5
Adding 6 to left hand side and the right hand side of the equation, it becomes
x - 6 + 6= - 5 + 6
x = 1
The sum of two numbers is 29
and their product is 180.
Find the numbers.
Final answer:
To find the two numbers with a sum of 29 and product of 180, we set up a system of equations, solve for one variable in terms of the other, and then factor a quadratic equation to find that the two numbers are 20 and 9.
Explanation:
The student's question is about finding two numbers based on their sum and product. To solve this, we can set up two equations based on the given information: let's call our numbers x and y. The first equation based on their sum is x + y = 29, and the second equation based on their product is xy = 180.
We can find one number in terms of the other using the first equation: y = 29 - x. We then substitute this into the second equation to get x(29-x) = 180. Simplifying, we have x² - 29x + 180 = 0. Factoring the quadratic equation, we get (x - 20)(x - 9) = 0, which gives us two possible values for x: 20 or 9. Thus, the two numbers are 20 and 9.
Tv emporium had a huge sale in the morning 5/12 of the flat screen televisions were sold in the afternoon one-third of the flat screen televisions were sold how many flat screen televisions were sold all together
Answer:
Total number of flat screen sold is 3/4
Step-by-step explanation:
Let the total number of the flat screen sold be y
y = number of flat screen sold in the morning + number of the flat screen sold in the afternoon.
Number sold in the morning = 5/15
Number sold in the afternoon = 1/3
Y = 5/12 + 1/3
Find the LCM of 12 and 3
Y = (5 + 4)/12
Y = 9/12
Y = 3/4
Total number of flat screen sold is 3/4
5/12
+1/3
=9/12
Reduce to 3/4
Step-by-step explanation:
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠E.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠E = °
Answer:
Step-by-step explanation:
Triangle DEF is a right angle triangle.
From the given right angle triangle,
DE represents the hypotenuse of the right angle triangle.
With m∠E as the reference angle,
EF represents the adjacent side of the right angle triangle.
DF represents the opposite side of the right angle triangle.
To determine m∠E, we would apply
the Tangent trigonometric ratio.
Tan θ = opposite side/adjacent side. Therefore,
Tan E = 8/5 = 1.6
E = Tan^-1(1.6)
W = 58.0° to the nearest tenth.
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠K.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠K = °
Answer:
Step-by-step explanation:
[tex]tan K=\frac{2}{3} \\m \angle K=tan^{-1} (\frac{2}{3} ) \approx 33.7 ^\circ[/tex]
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. y = x^2 +2x -5
Answer:
To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y -intercept(s): ( − 1 + √ 6 , 0 ) , ( − 1 − √ 6 , 0 ) y-intercept(s): ( 0 , − 5 )
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Three numbers, of which the third is equal to 12, form a geometric progression. If 12 is replaced with 9, then the three numbers form an arithmetic progression. Find these three numbers.
Final answer:
To find the three numbers, we determine 'a' and 'r' using a system of equations derived from the conditions that they form a geometric progression with 12 and an arithmetic progression with 9. By solving these equations, we obtain the three numbers in sequence.
Explanation:
The question requires us to find three numbers that form a geometric progression with the third being 12, and when the third number is changed to 9, the numbers form an arithmetic progression.
Let's denote the first number as 'a' and the common ratio of the geometric progression as 'r'. The three numbers in the geometric progression can be represented as 'a', 'ar', and 'ar^2'. Given that the third number is equal to 12, we have 'ar^2 = 12'.
When 12 is replaced with 9 to form an arithmetic progression, the common difference 'd' can be found by subtracting the first term from the second term. The three numbers in this sequence are 'a', 'a + d', and 'a + 2d'. Given that the third number is now 9, we have 'a + 2d = 9'.
To find 'a' and 'r', we can set up a system of equations using the fact that the second number in both progressions is the same. So 'ar = a + d'. We have the following system:
ar^2 = 12 (1)
a + 2d = 9 (2)
ar = a + d (3)
From equation (3), we can solve for 'd' in terms of 'a' and 'r': 'd = ar - a = a(r - 1)'. Substituting 'd' in equation (2), we get 'a + 2(a(r - 1)) = 9', which simplifies to 'a(2r + 1) = 9'.
Using this new equation along with equation (1), we solve for 'a' and 'r' to find the three numbers:
a(2r + 1) = 9 (4)
ar^2 = 12 (1)
From equation (1), 'a = 12/r^2'. Substituting this into equation (4) gives us a single equation: '12/r^2(2r + 1) = 9', which we can solve to find 'r', and subsequently, 'a'. After solving these, we find the three numbers that form both the geometric and arithmetic progressions.
To determine customer opinion of their safety features, Daimler - Chrysler randomly selects 110 service centers during a certain week and surveys all customers visiting the service centers. What type of sampling is used? a.Simple b.random c.Convenience d.Cluster e.Systematic f.Stratified
Simple sampling - A method where individuals are chosen randomly from a larger set.
Convenience sampling - The sample is being chosen as per ease of access thus it is not a random sampling.
Systematic sampling - Probability method where elements are chosen from a target population.
Stratified sampling - Method where population were divided into different groups called strata and the sample is then drawn from each group.
Cluster sampling - Population is where population were divided into different groups known as clusters. The clusters were then chosen randomly as the samples.
Answer: D (cluster sampling) - The service centers refer as the clusters and it is chosen randomly.
Final answer:
The Daimler - Chrysler survey method is an example of cluster sampling, where random groups (service centers) are selected and all members within these groups are surveyed.
Explanation:
The type of sampling used by Daimler - Chrysler when they randomly select 110 service centers during a certain week and survey all customers visiting those service centers is cluster sampling. In cluster sampling, the overall population is divided into groups, or clusters, and a random selection of these clusters is chosen.
All members (or customers, in this case) within these selected clusters are surveyed. This method is often more practical and cost-effective than surveying the entire population. It is important that the clusters themselves are representative of the population to ensure that data obtained is not biased.
There is a stack of sweaters at the store. Six sweaters have 5 buttons each. One sweater has 4 buttons. How many buttons do the sweaters have altogether?
Answer:
29 buttons
Step-by-step explanation:
6 x 5 - 1
Answer:
Step-by-step explanation: 29
A warehouse worker ships 25 boxes each day. Every box contains 3 shipping labels. Inventory has 500 shipping labels. How many days will it take to use the inventory of shipping labels? round to the nearest whole.
Answer: It will take 7 days to use the inventory of shipping labels.
Step-by-step explanation:
Given : Total boxes shipped by warehouse worker per day = 25
Every box contains 3 shipping labels.
Inventory has 500 shipping labels.
Then, the total number of boxes can be made = (Total shipping labels) ÷ (labels in each box)
500 ÷ 3 =166.67≈166
Number of days it will take to use the inventory of shipping labels= (total number of boxes can be made) ÷ (Total boxes shipped per day)
= 166÷ 25=6.64≈7
Hence, it will take 7 days to use the inventory of shipping labels.
It will take about 7 days to use the inventory of shipping labels.
Explanation:To find how many days it will take to use the inventory of shipping labels, we need to divide the total number of shipping labels by the number of shipping labels used per day.
The total number of shipping labels is 500 and the worker ships 25 boxes each day, with each box containing 3 shipping labels.
So, the worker uses 25 x 3 = 75 shipping labels per day.
Dividing the total number of shipping labels (500) by the number of shipping labels used per day (75), we get 500 / 75 = 6.67.
Rounding to the nearest whole number, it will take about 7 days to use the inventory of shipping labels.
2. An 82 kg man on a diving board drops from rest 3.0 m above the surface of the water
and he comes to rest 0.55 s after reaching the water. What is the average net force on
the diver as he is brought to rest? Remember to first find the velocity of the man after he
falls 3.0 m off of the diving board.
The average net force on the man as he is brought to rest is: F = -1143.9N
The man on the diving board has a potential energy, P.E = mghWhen the man dives, he has a kinetic energy, K.E = (1/2)mv²Therefore, P.E = K.E
mgh = (1/2)mv²82 × 9.8 × 3 = (1/2)× 82 × v²v² = 58.8V = 7.67 m/sWhen the man comes to rest, the final velocity becomes, 0.
As, such, acceleration which is the rate of change of velocity becomes;
a = (0 - 7.67)/0.55a = -13.95 m/s².The force on the man; F = mass × acceleration.
F = 82 × -13.95F = -1143.9NRead more:
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The average net force on the diver as he is brought to rest is approximately 689.56 N.
First, we can find the velocity of the man just before he reaches the water using the kinematic equation:
d = vt + 1/2at²
Now, let's calculate the velocity of the man just before he reaches the water using the equation:
vf=0+(−9.8m/s2)×0.782s≈−7.664m/s
Since the velocity is negative, it means the man is moving downward.
After entering the water, the man comes to rest in 0.55 seconds. During this time, he decelerates due to the force of gravity, but this time in the opposite direction to his motion. We can use the equation:
Finally, we can determine the average net force using Newton's second law:
Given that the mass m of the man is 82 kg, we find:
F net = 82 kg × 14.025 m/s 2 ≈ 1147.35 N
Therefore, the average net force on the diver as he is brought to rest is approximately 1147.35 N.
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x and y vary inversely, and y =7 when x = 4. What is the constant of variation?
Answer:
Y doesn't vary directly with x
Answer:28
Step-by-step explanation:
X varies inversely as y
X©1/y
X=k/y
4=k/7
Cross product
We get 4×7=k×1
28=k
Therefore constant (k)=28
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A jar contains 5 green, 3 black, and 2 red marbles. Brandi draws a marble from the jar and then puts it back. She then draws
another marble. What is the probability that Brandi draws
a. 2 greens
b. 2 reds
c. 1 black and 1 green
d. 1 green and 1 red
Step-by-step explanation:
a. 5/10 x 5/10 = 25%
b. 2/10 x 2/10 = 4%
c. 3/10 x 5/10 = 15% (Probability for getting black then green)
5/10 x 3/10 = 15% (Probability of getting green then black)
Thus, probability of getting green and black in any order is 30%
d. SIimilarly,
5/10 x 2/10 = 10% (Green then red)
2/10 x 5/10 = 10% (Red then green)
Green and red in any order 20%
Answer:
Depending on the remaining of the question. C is the answer
Step-by-step explanation:
5/10 x 5/10 = 25%
2/10 x 2/10 = 4%
3/10 x 5/10 = 15% Probability for getting black then green
5/10 x 3/10 = 15% Probability of getting green then black
green and black in any order is 30% the changes are higher in this case.
5/10 x 2/10 = 10% (Green then red)
2/10 x 5/10 = 10% (Red then green)
Green and red in any order 20%
A baker started out with 13 cups of flour.She had 9 and 1 four cups of flour left after the first batch of batter she made.She have 6 and 1 half cups of flour left after the second batch of batter she made.If she makes two more batches of batter,how many cups of flour will be left?
Question is wrong; Correct question is given below;
A baker started out with 12 cups of flour she had 9 1/4 cups of flour left after the first bunch of batter she made she had 6 1/2 cups of flour left after the second bunch of batter she made if she makes two more batches of batter how many cups of batter will be left?
Answer:
Baker will be left with 1 cups of Flour.
Step-by-step explanation:
Given
Amount of flour baker started with = 12 cups
Amount of flour left after making first batter = [tex]9\frac14\ cups[/tex]
[tex]9\frac14\ cups[/tex] can be Rewritten as [tex]\frac{37}4\ cups[/tex]
Amount of flour left after making first batter = [tex]\frac{37}4\ cups[/tex]
Now we can say that;
Amount of flour used to make first batter is equal to Amount of flour baker started with minus Amount of flour left after making first batter
Thus, the Amount of flour she use to make first batter = [tex]20-\frac{37}{4}[/tex]
Now we will use LCM to make the denominator common we get;
Amount of flour she use to make first batter = [tex]\frac{20\times4}{4}-\frac{37\times1}{4\times1} = \frac{48}{4}-\frac{37}{4}[/tex]
Now denominator common so we will solve the numerator we get;
Amount of flour she use to make first batter = [tex]\frac{48-37}{4}=\frac{11}{4}\ cups.[/tex]
Now Given:
Amount of flour left after the second batch of batter = [tex]6\frac12\ cups[/tex]
[tex]6\frac12\ cups[/tex] can be Rewritten as [tex]\frac{13}2\ cups[/tex]
Amount of flour left after the second batch of batter = [tex]\frac{13}2\ cups[/tex]
Thus, the quantity she use to make second batter = [tex]\frac{37}{4}-\frac{13}{2}[/tex]
Now we will use LCM to make the denominator common we get;
Amount of flour she use to make Second batter = [tex]\frac{37\times1}{4\times1}-\frac{13\times2}{2\times2}=\frac{37}{4}-\frac{26}{4}[/tex]
Now denominator common so we will solve the numerator we get;
Amount of flour she use to make Second batter = [tex]\frac{37-26}{4}=\frac{11}{4}\ cups[/tex]
Thus, she use [tex]\frac{11}{4}\ cups[/tex] of flour for each batter.
Amount of Flour used in making 2 more batter = [tex]2\times\frac{11}{4}= \frac{11}{2}\ cups[/tex]
Now we can say that;
Cups of flour left will be equal to Amount of flour left after the second batch of batter minus Amount of Flour used in making 2 more batter.
framing in equation form we get;
Cups of flour left = [tex]\frac{13}{2}-\frac{11}{2}=\frac{13-11}{2}=\frac{2}{2}=1\ cup[/tex]
Hence Baker will be left with 1 cups of Flour.
The equation R= -0.028t +20.8 can be used to predict the world record in the 200 meter dash, where R stands for the record in seconds and t for the number of years since 1920. In what year did the record become 19.68 seconds?
Final answer:
To find the year when the record became 19.68 seconds, substitute the value of R into the equation. Solve for t and add 1920 to get the year.
Explanation:
To find the year when the record became 19.68 seconds, we need to substitute the value of R into the equation:
R = -0.028t + 20.8
19.68 = -0.028t + 20.8
Solving for t:
Subtract 20.8 from both sides: -0.028t = -1.12
Divide both sides by -0.028: t = 40
Since t represents the number of years since 1920, we add 1920 to the result to get the year:
t + 1920 = 40 + 1920 = 1960
Therefore, the record became 19.68 seconds in the year 1960.
Lines a and b are parallel.
what is the measure of angle b
enter in the box
B=
Answer:
Ans _ angle b = 79
Hope it helps
∠B4 = ∠A2
b° = 79°
hope this helps :)
what is the graph of the inequality in the coordinate plane x ≥ 1
Answer: basically it would be whatever side the x is one indicating x is greater than 1
Step-by-step explanation:
I need help with this practice problem
Answer:
a. see below
b. Rita: 300; John: 900; Rodell: 925
c. Rita: L; John: 3L; Rodell: 3L+25
d. L +3L +(3L+25) = 2125
e. Rita: $600; John: $1800; Rodell: $1850
Step-by-step explanation:
Since John's number of laps is expressed in terms of Rita's number of laps, it makes a certain amount of sense to use Rita's laps as a unit of measure. We don't yet know what that unit of measure is, but we can use it to describe both John's laps and Rodell's laps. Rodell will have 25 additional laps added to the 3 units that match John's laps.
Altogether, these 7 units +25 laps will match the total of 2100 +25 laps. It is pretty clear that 1 unit will be 2100/7 = 300 laps. This is shown in the attachment.
__
a) The attachment matches the above description.
__
b) 1 unit of 300 laps is the number of laps Rita swam. Then John's 3 units correspond to 3×300 = 900 laps, and Rodell's laps will be 25 more than John's, so 925.
__
c) In this part, we define 1 unit as L, so the three contributors are ...
Rita: LJohn: 3LRodell: 3L+25__
d) The equation shows that the sum of the parts is equal to the whole:
L + 3L + (3L+25) = 2125
__
e) The numbers of part (b) get multiplied by $2, so are ...
Rita: $600John: $1800Rodell: $1850Estimate the value of the function at x = 4 given the following graph.
Yo sup??
The only way to solve this problem is by observing the graph closely and making some approximations.
We have to compare the value of x with the corresponding y value.
at x=4 you will find that the value of y is around 3.8-3.9
Therefore the answer is 3.8
Hope this helps.
Answer:
[tex]f(4) \approx 3.73[/tex]
Step-by-step explanation:
We can see that this function looks like a square root function but only shifted to the right by 1 and up by 2.
A square root function is:
[tex]f(x) = \sqrt{x}[/tex]
Shifting a function up means adding that value to the f(x):
[tex]f(x) = \sqrt{x}+2[/tex]
Shifting a function to the right means replacing a value x with the value (x-the value of shifting a function to the right):
[tex]f(x) = \sqrt{x-1}+2[/tex]
We can check that this really is a graph of a function [tex]f(x) = \sqrt{x-1}+2\\[/tex]:
[tex]f(1) = \sqrt{1-1}+2 = 0+2=2[/tex]
We can see on the graph that this really is the case : f(1)=2
Also,
[tex]f(2) = \sqrt{2-1}+2 = 1+2=3[/tex]
This is also the case if we check the graph.
So, now we have to estimate f(x) at x=4:
[tex]f(4) = \sqrt{4-1}+2 = \sqrt{3}+2[/tex]
where [tex]\sqrt{3} \approx 1.73[/tex] , hence:
[tex]f(4) \approx 1.73+2 = 3.73[/tex]
A very bright student is described as having an IQ that is three standard deviations above the mean. If this student's IQ is reported as a z-score, what would the z-score be?
a. z = m + 3
b. z = m + 3s
c. z = 3
d. cannot be determined from the information given
Answer:
Option C) z = 3
Step-by-step explanation:
We are given the following in the question:
IQ scores are normally distributed.
An IQ score is three standard deviations above the mean. Let x be the IQ score. Then, we can write,
[tex]x = \mu + 3\sigma[/tex]
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
[tex]z = \dfrac{\mu + 3\sigma-\mu}{\sigma} = \dfrac{3\sigma}{\sigma} = 3[/tex]
Thus, the z-score is 3.
Thus, the correct answer is
Option C) z = 3
The z-score for a student with an IQ three standard deviations above the mean would be z = 3.
Explanation:If a very bright student is described as having an IQ that is three standard deviations above the mean, and if this student's IQ is reported as a z-score, the z-score would be z = 3. This is because a z-score is a measure of how many standard deviations an observation is above or below the mean. When we say an observation is three standard deviations above the mean, we are describing a z-score of 3. Thus, the correct answer is c. z = 3.
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It usually took josh 2/5 of an hour to ride his bike to work. But on Monday, his bike was broken, so he took the bus to work which took 5/8 of an hour. How much longer was it to take the bus to work?
Final answer:
To find the difference in time, subtract the bike time from the bus time by finding a common denominator and subtracting the fractions.
Explanation:
To compare the time it took Josh to bike to work with the time it took him to take the bus, we need to subtract the bike time from the bus time.
The time it took Josh to bike to work is given as 2/5 of an hour. We can represent this as a fraction, 2/5.
The time it took Josh to take the bus is given as 5/8 of an hour. This can also be represented as a fraction, 5/8.
To find the difference, we subtract the bike time from the bus time: 5/8 - 2/5. To do this, we need a common denominator, which in this case is 40.
Multiplying the numerator and denominator of 5/8 by 5, we get 25/40. Multiplying the numerator and denominator of 2/5 by 8, we get 16/40.
Now we can subtract the fractions: 25/40 - 16/40 = 9/40.
Therefore, it took the bus 9/40 of an hour longer than it took Josh to bike to work.
Write a system of equations (3 points) for the problem below and then solve it The candy shack has 20 lb. Of mixed white and dark chocolate worth $7.50 per pound. White chocolate alone sells for $8.00 per pound and dark chocolate sells for 6.00 per pound. How many pounds of each are in the mixture?
Answer: the mixture contained 15 pounds of white chocolate and 5 pounds of dark chocolate.
Step-by-step explanation:
Let x represent the number of pounds of white chocolate in the candy shack mixture.
Let y represent the number of pounds of dark chocolate in the candy shack mixture.
The candy shack has 20 lb of mixed white and dark chocolate. This means that
x + y = 20
The 20lb mixture is worth $7.50 per pound. This means that the total cost of the mixture is
20 × 7.50 = $150
White chocolate alone sells for $8.00 per pound and dark chocolate sells for 6.00 per pound. This means that
8x + 6y = 150 - - - - - - - - - - - - - -1
Substituting x = 20 - y into equation 1, it becomes
8(20 - y) + 6y = 150
160 - 8y + 6y = 150
- 8y + 6y = 150 - 160
- 2y = - 10
y = - 10/ - 2
y = 5
x = 20 - y = 20 - 5
x = 15
In which of the following cases is productive efficiency not satisfied? Assume we start at a point on the PPF between two products. Select the correct answer below: The economy switches to producing less of one product without increasing the production of the other product. The economy switches to producing at the point of intersection of the PPF and the vertical axis. The economy switches to producing more of one product and less of the other product but remains on the PPF. The economy switches to producing at the point of intersection of the PPF and the horizontal axis.
Answer:
A. The economy switches to producing less of one product without increasing the production of the other product
Step-by-step explanation:
PPC is the graphical representation of product combinations that an economy can produce, given resources & technology. It is downward sloping because given resources & technology, production of a good can be increased by decreasing production of other good.
It is based on assumption that resources are efficiently utilised. Points on PPC show resources efficient utilisation, Points under PPC show under utilisation, Points outside PPC are beyond country's productive capacity.
If country produces less of a good without increasing production of other goods, implying wasted resources & production below PPC. This case doesn't satisfy productive efficiency
Other cases : Producing more of a good & less of other is just re allocative movement on the PPC itself. Production point at PPF intersection with either axis implies economy is producing only the good on that axis.
In all the cases except A. satisfy the 'productive efficiency'